On time-periodic solutions to an interaction problem between compressible viscous fluids and viscoelastic beams

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00602401" target="_blank" >RIV/67985840:_____/25:00602401 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1088/1361-6544/ad92f0" target="_blank" >https://doi.org/10.1088/1361-6544/ad92f0</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1361-6544/ad92f0" target="_blank" >10.1088/1361-6544/ad92f0</a>

Result language
angličtina
Original language name
On time-periodic solutions to an interaction problem between compressible viscous fluids and viscoelastic beams
Original language description
In this paper, we study a nonlinear fluid-structure interaction problem between a 'square-root' viscoelastic beam and a compressible viscous fluid. The beam is immersed in the fluid which fills a two-dimensional rectangular domain with periodic boundary conditions in both directions, while both the beam and the fluid are under the effect of time-periodic forces. By using a decoupling approach, at least one time-periodic weak solution to this problem is constructed which has a bounded energy and a fixed prescribed mass. The lack of a priori energy bounds is overcome by a series of estimates based on a careful choice of parameters. The most challenging one is the pressure estimate, which is obtained by utilizing the specific periodic geometry and the Bogovski operator on a fixed domain that has a uniform constant. With uniform estimates and improved regularity of the beam as in (Muha and Schwarzacher 2023Ann. Inst. Henri Poin. Anal. Non Lineaire 39 1369-412), the time-periodic solutionis constructed by a series of limit procedures, following the finite-dimensional time-space construction from (Feireislet al 2012 Arch. Rational Mech. Anal. 204 74586).
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA22-01591S" target="_blank" >GA22-01591S: Mathematical theory and numerical analysis for equations of viscous newtonian compressible fluids</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)